- #36
Dickfore
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andrien said:and I was thinking that feynman rules are derived first,then the gauge is fixed (which is supposed to be the key advantage of path integral formalism)
you were thinking wrong.
andrien said:and I was thinking that feynman rules are derived first,then the gauge is fixed (which is supposed to be the key advantage of path integral formalism)
In the path integral one has to plug in the Fadeev Popov determinant to fix the gauge. If I remember correctly, one after that the Feynman rules are derived.andrien said:and I was thinking that feynman rules are derived first,then the gauge is fixed (which is supposed to be the key advantage of path integral formalism)
You have to be careful; there are the so-called [itex]R_\xi[/itex] gauges which are a generalization of the Lorentz gauge [itex]\partial_\mu A^\mu = 0[/itex]; in the [itex]R_\xi[/itex] gauges one adds a gauge breaking term to the Lagrangian in the path integralandrien said:and I was thinking that feynman rules are derived first,then the gauge is fixed (which is supposed to be the key advantage of path integral formalism)
No,I am not and it is illustrated by tom.However I did not explained that i.e. the so called landau gauge and feynman gauge to which I was really referring.Dickfore said:you were thinking wrong.
Dickfore is right, and you were indeed thinking wrong!andrien said:No,I am not and it is illustrated by tom.However I did not explained that i.e. the so called landau gauge and feynman gauge to which I was really referring.
o.k. so maybe I thought about some specific parameter as gauge fixing and not the whole family of gauges which you have inherited in your mind.tom.stoer said:Dickfore is right, and you were indeed thinking wrong!
What I explained is that one does not fix a specific gauge but a class of gauges. But this IS essentially gauge fixing in the sense that the ∂μAμ family excludes other gauges like Coulomb gauge, axial gauge, Weyl gauge etc. So one could say that
1) one fixes a family of gauges labelled by a free parameter
2) derives the Feynman rules
3) fixes the parameter
Step 1) is gauge fixing!
?andrien said:... which you have inherited in your mind
tom.stoer said:Deriving the Feynman rules in the path integral formalism requires gauge fixing. But different gauge choices produce different sets of Feynman rules, so the propagators and vertices depend on the gauge. ... The most prominent example is the comparison of a non-abelian gauge theory like QCD ... In the Lorentz gauge the gauge fixing procedure "creates a new species of particles", so-called Fadeev-Popov ghosts which have their own propagators and vertices. These ghosts are absent in physical gauges like the axial gauge. ... that means that the particle content as defined by the Feynman diagrams of the theory differs between these gauges, whereas the particle content on the level of the physical Hilbert space ... is identical